Does it work?
A lot depends on how much you believe that muscle strength is involved in the development of bunions.
This is the short foot exercise (SFA):
The exercise is very effective for what it is designed for and that is to strengthen the intrinsic muscles of the foot. It is claimed to be an effective treatment for overpronation (its not). There is a bit of controversy around the SFA, most due to the extraordinary strength and number of claims that get made or what it can do, versus the lack of any actual evidence to support those claims.
Does it help those with bunions? Probably not. The problem with muscle strengthening in those with bunions is that due to the deformity (and the valgus of the hallux), the problem is not necessarily weak muscles, but a very poor lever arm that the intrinsic muscles have to exert their effect. This means that any gains from doing this exercise in those with bunions is going to be, at best, minimal in return for a extraordinary amount of effort and time needed to perform the exercise.
The exercise is a good adjunct to use in the treatment of plantar fasciitis.